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Journal of Homotopy and Related Structures

, Volume 13, Issue 1, pp 237–249 | Cite as

A note on orbit categories, classifying spaces, and generalized homotopy fixed points

  • Daniel A. Ramras
Article
  • 54 Downloads

Abstract

We give a new description of Rosenthal’s generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.

Keywords

Classifying space Family of subgroups Orbit category Homotopy fixed points 

Mathematics Subject Classification

Primary 55R35 Secondary 18F25 

Notes

Acknowledgements

The author thanks Jesper Grodal for pointing out earlier appearances of the category \(E_\mathcal {F}\Gamma \) in the literature, and Mark Ullmann and David Rosenthal for helpful comments. Additionally, the author thanks the referee and editor for helping to improve the exposition.

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndiana University-Purdue University IndianapolisIndianapolisUSA

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